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Solving the Equation (3x-1)(3x+1)-2x(1+4x)=-2
This article will guide you through the steps of solving the equation (3x-1)(3x+1)-2x(1+4x)=-2.
Step 1: Expand the equation
First, we need to expand the equation by multiplying out the brackets:
- (3x-1)(3x+1): This is a difference of squares pattern, so we can directly expand it as (3x)² - (1)² = 9x² - 1
- -2x(1+4x): Distribute the -2x, giving us -2x - 8x²
Now the equation becomes: 9x² - 1 - 2x - 8x² = -2
Step 2: Simplify the equation
Combine like terms on the left-hand side:
x² - 2x - 1 = -2
Step 3: Move all terms to one side
Add 2 to both sides to set the equation equal to zero:
x² - 2x + 1 = 0
Step 4: Factor the quadratic equation
The equation is now in a quadratic form. We can factor it:
(x - 1)(x - 1) = 0
Step 5: Solve for x
We have a repeated factor, (x - 1). Setting this factor equal to zero gives us:
x - 1 = 0
Adding 1 to both sides, we get:
x = 1
Solution
Therefore, the solution to the equation (3x-1)(3x+1)-2x(1+4x)=-2 is x = 1.